On the Existence of Solutions and Ulam-Type Stability for a Nonlinear <i>ψ</i>-Hilfer Fractional-Order Delay Integro-Differential Equation

On the Existence of Solutions and Ulam-Type Stability for a Nonlinear <i>ψ</i>-Hilfer Fractional-Order Delay Integro-Differential Equation

In this work, we address a nonlinear <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-Hilfer fractional-order Volterra integro-differential e...

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Bibliographic Details
Main Authors:	Cemil Tunç, Fehaid Salem Alshammari, Fahir Talay Akyıldız
Format:	Article
Language:	English
Published:	MDPI AG 2025-06-01
Series:	Fractal and Fractional
Subjects:	ψ-Hilfer FrOVI-DE unique solution UHR stability semi-UHR stability UH stability fixed-point approach
Online Access:	https://www.mdpi.com/2504-3110/9/7/409
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Summary:	In this work, we address a nonlinear <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-Hilfer fractional-order Volterra integro-differential equation that incorporates <i>n</i>-multiple-variable time delays. Employing the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-Hilfer fractional derivative operator, we investigate the existence of a unique solution, as well as the Ulam–Hyers–Rassias stability, semi-Ulam–Hyers–Rassias stability, and Ulam–Hyers stability of the proposed <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-Hilfer fractional-order Volterra integro-differential equation through the fixed-point approach. In this study, we enhance and generalize existing results in the literature on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-Hilfer fractional-order Volterra integro-differential equations, both including and excluding single delay, by establishing new findings for nonlinear <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-Hilfer fractional-order Volterra integro-differential equations involving <i>n</i>-multiple-variable time delays. This study provides novel theoretical insights that deepen the qualitative understanding of fractional calculus.
ISSN:	2504-3110